The first two terms of a progression are \(\sin^2\theta\) and \(\sin^2\theta\cos^2\theta\), for \(0<\theta<\pi/2\).

(a) If it is geometric, find the sum to infinity. [3]

Instead, it is arithmetic.

(b(i)) Find the common difference in terms of \(\sin\theta\). [3]

(b(ii)) Find the sum of the first 16 terms when \(\theta=\pi/3\). [3]